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[geometry] Preserve rotation axis signs at exact half turns #2191

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Merged
servantftransperfect merged 1 commit into from
Oct 6, 2026
Merged

[geometry] Preserve rotation axis signs at exact half turns #2191

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6 changes: 3 additions & 3 deletions src/aliceVision/geometry/lie.hpp
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Original file line number Diff line number Diff line change
Expand Up @@ -127,12 +127,12 @@ inline Eigen::Vector3d logm(const Eigen::Matrix3d& R)
Eigen::Matrix3d S = R + R.transpose() + (1.0 - R.trace()) * Eigen::Matrix3d::Identity();

Eigen::Vector3d signs;
// Use the sign of the biggest absolute values to define the rotation axis direction (its global sign)
if ( abs(p1) >= abs(p2) && abs(p1) >= abs(p3) )
// Use the largest diagonal entry to recover the axis signs, including at pi.
if (S(0, 0) >= S(1, 1) && S(0, 0) >= S(2, 2))
{
signs << SIGN(p1), SIGN(p1) * SIGN(S(1, 0)), SIGN(p1) * SIGN(S(2, 0));
}
else if ( abs(p2) >= abs(p1) && abs(p2) >= abs(p3) )
else if (S(1, 1) >= S(0, 0) && S(1, 1) >= S(2, 2))
{
signs << SIGN(p2) * SIGN(S(0, 1)), SIGN(p2), SIGN(p2) * SIGN(S(2, 1));
}
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46 changes: 46 additions & 0 deletions src/aliceVision/geometry/lie_test.cpp
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Expand Up @@ -12,6 +12,52 @@
#include <boost/test/tools/floating_point_comparison.hpp>
#include <aliceVision/unitTest.hpp>

#include <array>

BOOST_AUTO_TEST_CASE(SO3_logm_exact_half_turn)
{
using namespace Eigen;
using namespace aliceVision::SO3;

const std::array<Matrix3d, 7> rotations = {
(Matrix3d() << -1.0, 0.0, 0.0, 0.0, 0.0, -1.0, 0.0, -1.0, 0.0).finished(),
(Matrix3d() << -1.0, 0.0, 0.0, 0.0, -7.0 / 25.0, -24.0 / 25.0, 0.0, -24.0 / 25.0, 7.0 / 25.0).finished(),
(Matrix3d() << -7.0 / 25.0, -24.0 / 25.0, 0.0, -24.0 / 25.0, 7.0 / 25.0, 0.0, 0.0, 0.0, -1.0).finished(),
(Matrix3d() << 7.0 / 25.0, 0.0, -24.0 / 25.0, 0.0, -1.0, 0.0, -24.0 / 25.0, 0.0, -7.0 / 25.0).finished(),
(Matrix3d() << 1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, -1.0).finished(),
(Matrix3d() << -1.0, 0.0, 0.0, 0.0, 1.0, 0.0, 0.0, 0.0, -1.0).finished(),
(Matrix3d() << -1.0, 0.0, 0.0, 0.0, -1.0, 0.0, 0.0, 0.0, 1.0).finished()};

for (const Matrix3d& rotation : rotations)
{
const Vector3d algebra = logm(rotation);
BOOST_CHECK_SMALL(algebra.norm() - M_PI, 1e-12);
BOOST_CHECK_SMALL((expm(algebra) - rotation).norm(), 1e-12);
}
}

BOOST_AUTO_TEST_CASE(SO3_logm_near_half_turn)
{
using namespace Eigen;
using namespace aliceVision::SO3;

const std::array<Vector3d, 3> axes = {Vector3d(-4.0, 0.0, 3.0), Vector3d(3.0, -4.0, 0.0), Vector3d(0.0, 3.0, -4.0)};

for (const Vector3d& axis : axes)
{
for (double offset : {2e-3, 1e-3, 1e-6, 1e-8})
{
for (double direction : {-1.0, 1.0})
{
const Vector3d expected = direction * (M_PI - offset) * axis.normalized();
const Matrix3d rotation = AngleAxisd(direction * (M_PI - offset), axis.normalized()).toRotationMatrix();
const Vector3d algebra = logm(rotation);
BOOST_CHECK_SMALL((algebra - expected).norm(), 1e-7);
BOOST_CHECK_SMALL((expm(algebra) - rotation).norm(), 1e-7);
}
}
}
}

BOOST_AUTO_TEST_CASE(PoseFilter_lie_conversions)
{
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